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Dimensional Formula:
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Electrical resistivity (ρ) is a fundamental property of materials that quantifies how strongly they oppose the flow of electric current. It's defined as the resistance between opposite faces of a unit cube of the material.
The dimensional formula represents the physical quantity in terms of fundamental dimensions:
Where:
Explanation: This formula shows how resistivity depends on the fundamental physical quantities in the SI system.
From resistance formula: \( R = \rho \frac{L}{A} \)
Therefore: \( \rho = R \frac{A}{L} \)
Dimensional analysis:
- Resistance R has dimensions: \( [M^1 L^2 T^{-3} I^{-2}] \)
- Area A has dimensions: \( [L^2] \)
- Length L has dimensions: \( [L^1] \)
- Thus: \( \rho = [M^1 L^2 T^{-3} I^{-2}] \times [L^2] / [L^1] = [M^1 L^3 T^{-3} I^{-2}] \)
Details: The dimensional formula helps in:
• Verifying the correctness of physical equations
• Converting units between different systems
• Understanding the nature of physical quantities
• Deriving relationships between different physical quantities
Q1: What are the SI units of resistivity?
A: The SI unit of resistivity is ohm-meter (Ω·m).
Q2: How does resistivity differ from resistance?
A: Resistance depends on the material's dimensions, while resistivity is an intrinsic property independent of shape and size.
Q3: What factors affect resistivity?
A: Temperature, material composition, and impurities significantly affect resistivity. Most metals show increased resistivity with temperature.
Q4: Why is dimensional analysis important?
A: It helps verify equation consistency, derive relationships, and convert between unit systems.
Q5: What are typical resistivity values?
A: Conductors: ~10⁻⁸ Ω·m (copper), Semiconductors: ~10⁻⁵ to 10⁶ Ω·m, Insulators: ~10⁸ to 10¹⁶ Ω·m.